Najpierw wpisuję imię i nazwisko, a potem adres.

Because wpisuję means I enter / I fill in / I write into a form or field, not just I write in a general sense.

• pisać = to write
• wpisywać / wpisać = to enter, write in, fill in

In this sentence, the speaker is probably entering information on a form, website, or document, so wpisuję is the natural choice.

For example:

• Piszę list. = I am writing a letter.
• Wpisuję adres. = I am entering the address.

Wpisuję is:

• 1st person singular: I
• present tense
• from the verb wpisywać (imperfective)

So it literally means I am entering or I enter.

A few present-tense forms of wpisywać:

• wpisuję = I enter
• wpisujesz = you enter
• wpisuje = he/she/it enters
• wpisujemy = we enter

Yes — they are the direct objects of the verb, so they are in the accusative case.

However, in this sentence, their accusative forms happen to look the same as their nominative forms:

• imię → accusative imię
• nazwisko → accusative nazwisko
• adres → accusative adres

This is normal.

Why?

• imię and nazwisko are neuter nouns, and neuter singular nouns usually have the same nominative and accusative form.
• adres is a masculine inanimate noun, and those also usually have the same nominative and accusative form in the singular.

So the case does change grammatically, even though the word form does not visibly change.

Yes. Imię i nazwisko literally means first name and surname / name and last name.

• imię = first name / given name
• nazwisko = surname / last name

This is the standard Polish way to refer to someone’s full personal name in many everyday contexts, especially on forms.

Polish often leaves out possessive words like my, your, his, etc. when the meaning is obvious from context.

So:

• wpisuję imię i nazwisko naturally means I enter my first name and last name
• wpisuję adres naturally means I enter my address

If needed, Polish can add swój / swoje or a possessive pronoun, but it is often unnecessary and can sound less natural if the owner is obvious.

For example:

• Wpisuję imię i nazwisko. = I enter my first and last name.
• Wpisuję swoje imię i nazwisko. = I enter my own first and last name.
  This is possible, but usually not needed.

They mean:

• najpierw = first / at first / first of all
• potem = then / afterwards / later

Together they help show sequence:

• Najpierw wpisuję imię i nazwisko, a potem adres. = First I enter my first and last name, and then the address.

These are very common words for describing steps or instructions.

You could also see:

• Najpierw... potem...
• Najpierw... a potem...

Both are common.

In Polish, a often connects two parts of a sentence by showing a contrast or a step-by-step progression. Here it sounds very natural in a sequence:

• najpierw ... a potem ... = first ... and then ...

Using i potem is not impossible in some contexts, but a potem is much more idiomatic here.

Compare:

• Najpierw jem obiad, a potem piję kawę.
  = First I eat lunch, and then I drink coffee.

So in this sentence, a is the natural connector between the two stages.

Yes, Polish word order is more flexible than English word order, although some versions sound more natural than others.

The given sentence:

• Najpierw wpisuję imię i nazwisko, a potem adres.

is very natural and neutral.

You could also say:

• Imię i nazwisko wpisuję najpierw, a potem adres.

But this sounds more marked, as if you are emphasizing imię i nazwisko.

So the original order is probably the best one for a learner to use.

Yes. Wpisuję is imperfective.

That is natural here because the sentence describes a process or a sequence of actions in a general way:

• Najpierw wpisuję..., a potem... = First I enter..., then...

The perfective partner is wpisać, and its 1st person singular future form is wpiszę.

Compare:

• wpisuję = I am entering / I enter
• wpiszę = I will enter / I will have entered

In instructions, demonstrations, or descriptions of what someone does on a form, wpisuję is the expected choice.

A rough pronunciation guide:

• imię ≈ EE-myeh
  The ę here is often pronounced very lightly, and in everyday speech at the end of a word it may sound close to e.

• nazwisko ≈ naz-VEES-ko
  Stress is on the second-to-last syllable: -wis-

• wpisuję ≈ fpee-SOO-yeh
  The initial w in Polish sounds like English v, but after voiceless consonants it may sound closer to f in actual pronunciation.

A few useful sound notes:

• w = usually like English v
• sz = like sh
• rz/ż = like the s in measure or the zh sound
• ę = a nasal vowel, though its exact pronunciation changes depending on position

Adres usually means address, especially a postal address, home address, email address, or web address depending on context.

In this sentence, it most likely means a mailing or home address because it appears with personal information:

• imię i nazwisko
• adres

So the sentence sounds like something you would see when filling out a form.